ine segment AB has endpoints A(–4, –10) and B(–11, –7). To find the x-coordinate of the point that divides the directed line segment in a 3:4 ratio, the formula x = (x2 – x1) + x1 was used to find that x = (–11 – (–4)) + (–4).
Therefore, the x-coordinate of the point that divides AB into a 3:4 ratio is

Answer:

45.73 m

Step-by-step explanation:

Answer:

Step-by-step explanation:

A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario?

f(x) = 1500(1.15)x  

f(x) = 1500(115)x

f(x) = 1500(2.15)x

f(x) = 1500(215)x

The answer to this problem is a f(x) = 1500(2.15)x

Answer:

[tex]f(x) = 1500(2.15)^x[/tex]

Step-by-step explanation:

Let the function that represents the population of bacteria after x hours is,

[tex]f(x)=ab^x[/tex]

For x = 0, f(x) = 1500,

[tex]1500=a(1+r)^0[/tex]

[tex]1500=a[/tex]

Now, the population increases at a rate of 115% each hour,

So, the population after 1 hour = (100+115)% of 1500 = 215% of 1500 = 3225,

That is, for x = 1, f(x) = 3225,

[tex]3225 =ab[/tex]

[tex]3225=1500(b)[/tex]

[tex]\implies b =2.15[/tex]

Hence, the function that represents the given scenario is,

[tex]f(x)=1500(2.15)^x[/tex]

Answer:

common Joe is cheaper

Step-by-step explanation:

1500/200 =7.5 truckloads

7.5×50=$375

1500/90=16.666 truckloads

16.666×20=$333.

I really didn't know for sure what u we're looking for

Answer:Common Joe

Step-by-step explanation:

Given

Total weight of Raw material is 1500 tons

Big Red can transport 200 tons at a cost of $50 per truckload

so  Big Red need to do 8 rounds to completely transport the raw material

In first 7 round round it carries 200 tons and in last round it carry 100 tons

i.e. [tex]200\times 7+100[/tex]

so cost for Red bus=[tex]50\times 8=$400[/tex]

For Common Joe truck requires 17 round of loading to completely transport 1500 tons

In first 16 round it carries 90 tons and in last round it carries 60 tons

So cost for Common Joe is [tex]17\times 20=$340[/tex]

So Factory should choose Common Joe while considering Economy.

Answer: 14

Step-by-step explanation:

Answer:

The y-intercept is: (0,14).

Answer:

0 and 1 have the same y values for the x values.

Answer:

-3/2

Step-by-step explanation:

(Y2-Y1)/(X2-X1)

(-4 - 5) / (4 - (-2))

-9 / 6

Simplified: -3/2

Answer:

-3/2

Step-by-step explanation:

Answer:

c. 5

Step-by-step explanation:

Because 15 divided by 3 equals 5

So 25 divided by 5 equals 5 (dont know if it is correct)

From concept of similar triangles, the value of x is Option (C) 5 .

Similar triangles are triangles that have the same shape but their sizes, dimensions may vary. All equilateral triangle, squares of any shape are example of similar objects. If two triangles are similar triangles then their corresponding angles are congruent and the corresponding sides are in equal proportion.  

We know from concept of similar triangles, the corresponding sides are in equal proportion.

Both the triangle given in the diagram are similar.

The unknown side given is x .

Using proportion concept,

⇒  [tex]\frac{15}{3} = \frac{25}{x}[/tex]

⇒  [tex]x = \frac{25}{5}[/tex]

∴   [tex]x = 5[/tex]

Thus, From concept of similar triangles, the value of x is Option (C) 5.  

To learn more about concepts of similar triangles, refer -

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Answer:

-4g-3

------------

g+2

Step-by-step explanation:

g+1                     5g+4

-------------  -   ------------------

g+2                     g+2

Since the denominators are the same, subtract the numerators

g+1 - (5g+4)

Distribute the negative sign

g+1 -5g-4

-4g-3

Put this back over the denominator

-4g-3

------------

g+2

Answer:

-4g-3, g+2

Step-by-step explanation:

ANSWER

The base is 7 and the height is 9.

EXPLANATION

If we consider any two pairs of points and the y-coordinates of these two points are constant (are the same), then that side forms one of the bases of the rectangle.

Consider, Q(-1, 1) and R(6, 1)

The y-values are the same.

The base of the rectangle is the absolute value of difference in the x-values.

[tex]Base = |6 - - 1| = |7| = 7[/tex]

We could have also used S(6,-8), and T(-1,-8) to obtain the same result.

For R(6, 1) and S(6,-8), the x-coordinates are the same. The height is the absolute values of difference in the y-values.

[tex]Height= |1 - - 8| = |9| = 9[/tex]

Therefore, the base is 7 and the height is 9.

Answer:

Base is 7, and Height is 9.

Step-by-step - If we consider any two pairs of points and the y-coordinates of these two points are constant (are the same), then that side forms one of the bases of the rectangle.

Consider, Q(-1, 1) and R(6, 1)

The y-values are the same.

The base of the rectangle is the absolute value of difference in the x-values.

We could have also used S(6,-8), and T(-1,-8) to obtain the same result.

For R(6, 1) and S(6,-8), the x-coordinates are the same. The height is the absolute values of difference in the y-values.

Therefore, the base is 7 and the height is 9.

Answer:

53+47

Step-by-step explanation:

100-53 is 47. 53-47 gives you 6

Answer:

The numbers are 53 and 47.

Step-by-step explanation:

You didn't write out the problem completely, but this may be the problem:

The sum of two numbers is 100. The difference of the two numbers is 6. What are the numbers?

Let the numbers be x and y.

The sum of two numbers is 100.

x + y = 100

The difference of the two numbers is 6.

x - y = 6

We have a system of two equations in two variables.

x + y = 100

x - y = 6

Add the equations.

2x = 106

x = 53

Now substitute 53 for x in the first equation and solve for y.

53 + y = 100

Subtract 53 from both sides.

y = 47

The numbers are 53 and 47.

Answer:  4.7

Step-by-step explanation:

Use Soh Cah Toa

[tex]sin \theta=\dfrac{opposite}{adjacent}\\\\\\sin(58^o)=\dfrac{4.0}{x}\\\\\\x=\dfrac{4.0}{sin(58^o)}\\\\\\x=4.7[/tex]

Answer:

The value of x = 4.7

Step-by-step explanation:

From the figure we can see aright triangle with height = 4.0 and one angle is 58°

Points to remember

Trigonometric ratios

Sin θ  = Opposite side/Hypotenuse

To find the value of x

Sin 58 = Opposite side/Hypotenuse

 = 4/x

x = 4/Sin (58)

 = 4/0.848

 = 4.71 ≈ 4.7

Therefore the value of x = 4.7

I will convert feet to inches.

4 feet, 6 inches = 54 inches

20 feet = 240 inches

5/x = 54/240

Let x = closest height of tree

54x = 5(240)

54x = 1,200

x = 1200/54

x = 22.2222222222

The tree is about 22 feet tall.

Answer:

22 inches

Step-by-step explanation:

Height of Mac = 5 feet

Height of shadow of Mac = 4 foot 6 inches = [tex]4+\frac{6}{12}= 4.5[/tex] inches .

We are given that At the same time, a nearby tree casts a 20  foot shadow .

Let the height of the tree be x

ATQ

[tex]\frac{5}{4.5}=\frac{x}{20}[/tex]

[tex]\frac{5}{4.5} \times 20=x[/tex]

[tex]22.22=x[/tex]

Hence the height of the tree is approximately 22 inches .

Answer:

30

Step-by-step explanation:

  40

x 0.75

-----------

=  30

Answer:

[tex]\sum_{n=1}^{10} 316.5 (1.055)^{n-1} [/tex]

Step-by-step explanation:

The amount (A) in a deposit after 1 year is calculated as follows:

A = P*(1 + r)

where:

P is the present value

r is the annual rate (decimal)

After the first year:

A = 300*(1 + 0.055) = $316.5

After the second year, the account will have a new amount of $316.5 due to the new $300 and the interest gained with the previous $316.5:

A = 316.5 + 316.5*(1 + 0.055)

After the third year:

A = 316.5 + [316.5 + 316.5*(1 + 0.055)]*(1 + 0.55)

A = 316.5 + 316.5*(1 + 0.055) + 316.5*(1 + 0.055)^2

After 10 years:

[tex]\sum_{n=1}^{10} 316.5 (1.055)^{n-1} [/tex]

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept (0, b)

We have the slope m = -9 and the y-intercept (0, -2) → b = -2.

Substitute:

y = -9x + (-2) = -9x - 2

Answer:

A

Step-by-step explanation:

458,700 = 4.587 * 10^5

Answer:

A

Step-by-step explanation:

Answer:

A; 4,6,8

Step-by-step explanation:

Answer:

angles 4,6,8

Step-by-step explanation: Did it on i-ready and got it right.

Answer:

That's incorrect. The simplest way to show this is by evaluating the functions at a given point. Let's say x=0, then:

Sin(-x) = Sin(0) = 0

-cos x = -cos (0) = -1

Therefore, Sin(-x)≠-cos x.

The given expression :

        [tex]\sin (-x)=-\cos x[/tex] is a false expression i.e. it is not true for all the values of x.

We are asked to check whether the trignometric expression is true for all the values of x or not.

The expression is given by:

[tex]\sin (-x)=-\cos (x)[/tex]

We consider x=0

Then on taking left hand side of the expression we have:

[tex]\sin (-0)\\\\i.e.\\\\\sin (0)\\\\=0[/tex]

and the right hand side of the expression is:

[tex]-\cos x\\\\i.e.\\\\-\cos 0\\\\i.e.\\\\-1[/tex]

i.e. we have:

[tex]0=-1[/tex]

which is false.

Hence the statement is not true for all the values of x.

Answer:  [tex]\bold{\sqrt[8]{2^7} }[/tex]

Step-by-step explanation:

[tex]\sqrt[4]{2} \times \sqrt[8]{2} \times \sqrt[2]{2}\\\\={2^{\frac{1}{4}}\times 2^{\frac{1}{8}}\times 2^{\frac{1}{2}}\\\\=2^{\frac{1}{4}+\frac{1}{8}+\frac{1}{2}}\\\\=2^{\frac{2}{8}+\frac{1}{8}+\frac{4}{8}}\\\\=2^{\frac{7}{8}}\\\\\\=\large\boxed{\sqrt[8]{2^7}}[/tex]

Answer:  78.8 ft

Step-by-step explanation:

Similar triangles have proportional sides.

[tex]\dfrac{\text{building shadow}}{\text{building height}}=\dfrac{\text{flagpole shadow}}{\text{flagpole height}}\\\\\\\dfrac{35}{\text{building height}}=\dfrac{8}{18}\\\\\\\dfrac{35\times 18}{8}=\text{building height}\\\\\\\dfrac{35\times 9}{4}=\text{building height}\\\\\\\dfrac{315}{4}=\text{building height}\\\\\\\boxed{78.75=\text{building height}}[/tex]

Answer:

25/169

Step-by-step explanation:

We have 13 marbles ( 5+6+2)

P (blue ) = blue marbles/ total marbles = 5/13

P (blue ,blue) = 5/13* 5/13  since the marble is replaced

                      = 25/169

Answer:

arrow going from 9 to -infinity (open circle)

Step-by-step explanation:

equalize equation by multiplying both sides by 3 to obtain the equation 9>t

then simply plug in numbers to see if they check out, ie: 3> 4/3 makes sense, but 3> 10/3 doesn't.

Draw the arrow to accommodate for the answers that DO fit.

open circle, because it doesn't work for t=9

Answer:

see below

Step-by-step explanation:

3 > t/3

Multiply each side by 3

3*3 > t/3 *3

9 > t

t < 9

There is an open circle at 9, since  the symbol is  less than

The line goes to the left.

Answer:

Option D is correct.

Step-by-step explanation:

The additive inverse of a number is the same number with the negative sign

i.e. if we have a number 1 then it's additive inverse would be -1

So if we add both the number and its additive inverse the answer would be zero.

1+(-1) = 0

So, Option D their sum is always zero is correct.

Answer: Option D

Their sum is always zero

Step-by-step explanation:

Given any number x, the additive inverse of x is -x.

For example, the additive inverse of 3 is - 3, the additive inverse of 2.2 is -2.2.

In this way, note that adding a number with the additive inverse of this number will always result in the number zero.

[tex]x + (-x) = 0[/tex]

Therefore, the correct option is option D

Answer:100

Step-by-step explanation:

That is the most common number

Hello There!

Mode: The number that occurs most often in a set of numbers

in this case, the number 100 occurs more than any other number in the set.  This means that the mode for this set of data is 100.

Answer:

√a(√a + 2)          a - 2√a

----------------- = -----------------

    a - 4                a - 4

Step-by-step explanation:

I am assuming that by "sqrt(a)/sqrt(a)-2" you meant:

√a

----------

√a - 2

To rationalize the denom., multiply numerator and denom. of this fraction by the conjugate of √a - 2, which is √a + 2:

√a(√a + 2)

-----------------

    a - 4

For this case we must find an expression equivalent to:

[tex]16 ^ 3[/tex]

We can rewrite 16 as [tex]2 * 2 * 2 * 2 = 2 ^ 4[/tex]

Rewriting the expression we have:

[tex](2 ^ 4) ^ 3 =[/tex]

By definition of power properties we have to:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

So, we have:

[tex](2 ^ 4) ^ 3 = 2 ^ {12}[/tex]

Answer:

Option C

Answer:

C

Step-by-step explanation:

edg2021

Check the picture below.  The picture is using feet, but is pretty much the same trajectory for meters.

so the object hits the ground when y = 0, thus

[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in meters} \\\\ h(t) = -4.9t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{12}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{62.5}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\\\ h(t)=-4.9t^2+12t+62.5\implies \stackrel{\textit{hitting the ground}}{\stackrel{h(t)}{0}=-4.9t^2+12t+62.5}[/tex]

[tex]\bf ~~~~~~~~~~~~\textit{using the quadratic formula} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-4.9}t^2\stackrel{\stackrel{b}{\downarrow }}{+12}t\stackrel{\stackrel{c}{\downarrow }}{+62.5} \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ t=\cfrac{-12\pm\sqrt{12^2-4(-4.9)(62.5)}}{2(-4.9)}\implies t=\cfrac{-12\pm\sqrt{144+1225}}{-9.8} \\\\\\ t=\cfrac{12\mp\sqrt{1369}}{9.8}\implies t=\cfrac{12\mp 37}{9.8}\implies t= \begin{cases} \stackrel{\approx}{-2.55}\\ 5 \end{cases}[/tex]

we can't use -2.55, since it's seconds and can't be negative, so t = 5 seconds later.

Answer:

optain A or the first one

Step-by-step explanation:

hop this helps

Finding 80% of 630 doesn't require using a table and can be calculated by simply multiplying 0.80 by 630 which gives 504.

To determine 80% of 630, Allison doesn't necessarily need a table. However, we can illustrate the solution using a simple self-created table. The calculation is rather straightforward. If Allison wants to find 80% of 630, she can simply multiply 0.80 (which is the decimal equivalent of 80%) by 630.

Therefore, 80% of 630 is 504.

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Answer: Last option.

Step-by-step explanation:

To find which expression in equivalent to the expression [tex]\frac{125^2}{125^\frac{4}{3} }[/tex], you need to remember  :

The Power of a power property:

[tex](a^m)^n=a^{(mn)}[/tex]

The Quotient of powers property:

[tex]\frac{a^m}{a^n} =a^{(m-n)}[/tex]

And the Product of powers property:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

Knowing that:

 [tex]125=5*5*5=5^3[/tex]

Then, you get:

[tex]\frac{125^2}{125^\frac{4}{3} }=\frac{(5^3)^2}{(5^3)^\frac{4}{3} }=\frac{5^6}{5^4}=5^{(6-4)}=5^2=25[/tex]

Answer:

x = -2 and y = 3

Step-by-step explanation:

It is given that,

4x + 5y = 7    -----(1)

3x – 2y = –12   ----(2)

To find the value of x and y

eq(1) * 3 ⇒

12x + 15y = 21   ----(3)

eq(2) * 4 ⇒

12x - 8y = -48  ---(4)

eq(3) - eq(4) ⇒

12x + 15y = 21   ----(3)

12x - 8y = -48 ---(4)

 0 + 23y = 69

y = 69/23 = 3

Substitute the value of y in eq(1)

4x + 5y = 7    ----(1)

4x + 5*3 = 7

4x = 7 - 15 = -8

x = -8/4 = -2

Therefore x = -2 and y = 3

Answer:

x = -2 and y = 3

Step-by-step explanation: